**Problems on Trains with Solutions 1 :**

This is the continuity of our web content "Problems on Trains".

Before look at the problems on trains, if you would like to know the shortcuts which are required to solve problems on trains,

**Problem 1 :**

Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet ?

**Solution :**

Let the trains meet each other "m" hours after 7 a.m.

Distance covered by the train from A in "m" hrs is

= Speed ⋅ Time

= 20 kms

At a particular time after 8 a.m, if the train from A had traveled "m" hours, then the train from B would have traveled (m-1) hours.

Because it started at 8.00 am. (one hour later)

Distance covered by the train from B in (m - 1) hrs is

= 25(m - 1)

At the meeting point,

sum of the distances covered by the two trains is equal to the total distance (from A to B).

That is

20m + 25(m-1) = 110

20m + 25m - 25 = 110

45m = 135

m = 3 hours

So, two trains meet each other 3 hrs after 7 a.m

That is, at 10 a.m.

Hence, the time at which they will meet is 10 a.m.

**Problem 2 :**

Two trains are running at 40 kmph and 20 kmph respectively in the same direction .Faster train completely passes a man who is sitting in the slower train in 9 seconds. What is the length of the faster train?

**Solution :**

Relative speed of two trains is

= 40 - 20

= 20 kmph

= 20 ⋅ 5/18 m/sec

= 50/9 m/sec

**Given :** Faster train completely passes a man who is sitting in the slower train in 9 seconds.

Length of the faster train is

= The distance covered by the faster train in this 9 seconds

= Speed ⋅ Time

= 50/9 ⋅ 9

= 50 m

Hence, the length of the faster train is 50 m.

**Problem 3 :**

Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. Find the ratio of their speeds

**Solution :**

Let "a" m/sec and "b" m/sec be the speeds of two trains respectively

First train crosses the man in 27 seconds with speed "a" m/sec

So, the length of the first train is

= Distance covered in 27 seconds

= Speed ⋅ Time

= a ⋅ 27

= 27a -----(1)

Second train crosses the man in 17 seconds with speed "b" m/sec

Length of the second train is

= Distance covered in 17 seconds

= Speed ⋅ Time

= b ⋅ 17

= 17b -----(2)

**Given :** The given two trains cross each other in 23 seconds.

The distance covered by the two trains in this 23 seconds is

= Sum of the lengths of the two trains

= Relative speed ⋅ Time

= (a + b) ⋅ 23

= 23a + 23b -----(3)

We know the fact that when two trains cross each other in opposite directions, the distance covered by them is equal to sum of the length of the two trains.

That is,

(1) + (2) = (3)

27a + 17b = 23a + 23b

4a = 6b

a / b = 6 / 4

a / b = 3 / 2

a : b = 3 : 2

Hence, the ratio of their speeds is 3:2.

**Problem 4 :**

A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform ?

**Solution :**

Speed of the train = 54 kmph

= 54 ⋅ 5/18 m/sec

= 15 m/sec

The train passes the man in 20 seconds.

The distance covered by the train in this 20 seconds is equal to the length of the train.

Distance = Speed ⋅ Time

Distance = 20 ⋅ 15

Distance = 300 m

So, length of the train is 300 m.

Let "m" be the length of the platform

**Given :** The train crosses the platform in 36 seconds.

We know the fact that the distance covered by the train in this 36 seconds is equal to sum of the lengths of the train and platform

Then, the distance covered by the train in 36 seconds is

= 300 + m

So, the train takes 36 seconds to cover the distance "300 + m"

Time = Distance / Speed

36 = (300 + m) / 15

540 = 300 + m

240 = m

Hence, the length of the platform is 240 meters.

**Problem 5 :**

Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. Find the time taken by the two trains to cross each other.

**Solution :**

Relative speed is

= 60 + 90 = 150 kmphr

= 150 ⋅ 5/18 m/sec

= 125/3 m/sec

When they cross each other, distance covered by both the trains is equal to sum of the lengths of the two trains.

So, the distance covered by them is

= 1.1 + 0.9

= 2 km

= 2 ⋅ 1000 m

= 2000 m

Time taken by the two trains to cross each other is

= Distance / Speed

= 2000 / (125/3)

= 2000 ⋅ 3/125

= 48 seconds

Hence, time taken by the two trains to cross each other is 48 seconds.

Apart from the problems given above, if you need more problems on trains, please click the following links.

**Problems on Trains with Solutions**

**Problems on Trains with Solutions - 2**

After having gone through the stuff given above, we hope that the students would have understood, how to solve problems on trains with solutions.

Apart from the stuff, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**

**Sum of all three four digit numbers formed using 0, 1, 2, 3**

**Sum of all three four digit numbers formed using 1, 2, 5, 6**

HTML Comment Box is loading comments...